scholarly journals Computationally efficient expression for the zero-temperature isotherm in equations of state

1980 ◽  
Author(s):  
B Bennett
Keyword(s):  
Equations Of State ◽  
Zero Temperature ◽  
Computationally Efficient ◽  
Temperature Isotherm ◽  
Efficient Expression

scholarly journals Evaluating the Observed Log-Likelihood Function in Two-Level Structural Equation Modeling with Missing Data: From Formulas to R Code

Psych ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 197-232
Author(s):  
Yves Rosseel
Keyword(s):  
Structural Equation ◽  
Structural Equation Models ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Missing At Random ◽  
Equation Modeling ◽  
Computationally Efficient ◽  
Log Likelihood ◽  
Efficient Expression ◽  
Special Case

This paper discusses maximum likelihood estimation for two-level structural equation models when data are missing at random at both levels. Building on existing literature, a computationally efficient expression is derived to evaluate the observed log-likelihood. Unlike previous work, the expression is valid for the special case where the model implied variance–covariance matrix at the between level is singular. Next, the log-likelihood function is translated to R code. A sequence of R scripts is presented, starting from a naive implementation and ending at the final implementation as found in the lavaan package. Along the way, various computational tips and tricks are given.

Fast Algorithms of Line Outage Distribution Factors with Cascading Failures

2014 ◽  
Vol 1070-1072 ◽  
pp. 843-848
Author(s):  
Xiao Long Fan ◽  
Jin Quan Zhao
Keyword(s):  
Fast Algorithms ◽  
Computationally Efficient ◽  
Double Line ◽  
Cascading Outages ◽  
Security Applications ◽  
Multiple Line ◽  
Recursive Theory ◽  
Efficient Expression ◽  
Line Outages

The prominent role of cascading outages in recent blackouts has created a need in security applications for evaluating line outage distribution factors (LODFs) under the multiple-line outages. Two fast algorithms of LODFs with multiple-line outages are proposed in this paper. In the first method, the double-line outage LODFs are expressed in terms of single-line outage LODFs, and it can be extended to N-k (k≥2) contingencies without any complex matrix operation through the recursive theory. In the second method, a computationally efficient expression of LODFs based on power transfer distribution factors (PTDFs) in pre-contingency network is presented. Numerical simulations are carried out on IEEE 14 and 118-bus test systems. The results show that both methods can effectively improve the computation speed of multiple-line outage LODFs.

scholarly journals Relativistic Neutron Stars: Rheological Type Extensions of the Equations of State

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 189
Author(s):  
Alexander Balakin ◽  
Alexei Ilin ◽  
Anna Kotanjyan ◽  
Levon Grigoryan
Keyword(s):  
Neutron Star ◽  
Neutron Stars ◽  
Equations Of State ◽  
Pressure Profile ◽  
Spherically Symmetric ◽  
Zero Temperature ◽  
New Approach ◽  
Modified Equations

Based on the Rheological Paradigm, we extend the equations of state for relativistic spherically symmetric static neutron stars, taking into consideration the derivative of the matter pressure along the so-called director four-vector. The modified equations of state are applied to the model of a zero-temperature neutron condensate. This model includes one new parameter with the dimensionality of length, which describes the rheological type screening inside the neutron star. As an illustration of the new approach, we consider the rheological type generalization of the non-relativistic Lane–Emden theory and find numerically the profiles of the pressure for a number of values of the new guiding parameter. We have found that the rheological type self-interaction makes the neutron star more compact, since the radius of the star, related to the first null of the pressure profile, decreases when the modulus of the rheological type guiding parameter grows.

TWO EQUATIONS OF STATE CONSIDERING THE THERMAL EFFECT FOR α, β AND ω PHASES OF ZIRCONIUM

2008 ◽  
Vol 22 (03) ◽  
pp. 167-180
Author(s):  
RONGGANG TIAN ◽  
JIUXUN SUN ◽  
CHAO ZHANG ◽  
FULONG WANG
Keyword(s):  
Experimental Data ◽  
Thermal Effect ◽  
Equations Of State ◽  
Zero Point ◽  
Hexagonal Structure ◽  
Zero Temperature ◽  
Β Phase ◽  
Ω Phase ◽  
Α Phase ◽  
Einstein Model

The Baonza and mGLJ equations of state (EOS) modified previously to consider the thermal effect are applied to study the thermodynamic properties of Zirconium (Zr) . It is proposed that the zero-point vibration term should be deleted in a thermal EOS, and the parameters cannot be directly taken as experimental data at a reference temperature, [Formula: see text] and [Formula: see text], but their values at absolute zero temperature, [Formula: see text] and [Formula: see text]. Based on the Einstein model, an approach is proposed to solve [Formula: see text] and [Formula: see text] from [Formula: see text] and [Formula: see text]. For the hcp (α phase), bcc (β phase) and hexagonal structure (ω phase) of Zr , the molar volume (V), isothermal bulk modulus (B) and thermal expansion coefficient (α) was calculated as a function of pressure and temperature. The predictive capabilities of the complete EOS are discussed and compared with experimental data.

WARM STELLAR MATTER: APPLICATION TO SLOWLY ROTATING COMPACT OBJECTS

2008 ◽  
Vol 23 (05) ◽  
pp. 729-740
Author(s):  
M. D. ALLOY ◽  
D. P. MENEZES
Keyword(s):  
Equations Of State ◽  
Compact Objects ◽  
Zero Temperature ◽  
Stellar Matter

In the present paper we investigate one possible variation on the usual static pulsars: the inclusion of rotation. We use a formalism proposed by Hartle and Thorne to calculate the properties of rotating pulsars with all possible compositions. The calculations were performed for both zero temperature and for fixed entropy equations of state.

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